Remove shadow/background glow on highcharts data label?

Set dataLabels.styles.textShadow to false.

    plotOptions: {
        columnrange: { // or general options: "series: { ... }"
            dataLabels: {
                enabled: true,
                color: 'red',
                style: {
                    textShadow: false 
                }
            }
        }
    },

Demo: http://jsfiddle.net/oe1vcmqj/2/

EDIT:

Since Highcharts 5.0.3, the option name is textOutline.

    plotOptions: {
        columnrange: { // or general options: "series: { ... }"
            dataLabels: {
                enabled: true,
                color: 'red',
                style: {
                    textOutline: false 
                }
            }
        }
    },

Demo: http://jsfiddle.net/oe1vcmqj/49/

EDIT v2.0:

Since Highcharts 5.0.13, the textOutline option should be a string, so to disable outline, set textOutline: 'none'.

    plotOptions: {
        columnrange: { // or general options: "series: { ... }"
            dataLabels: {
                enabled: true,
                color: 'red',
                style: {
                    textOutline: 'none' 
                }
            }
        }
    },

Demo: http://jsfiddle.net/BlackLabel/s7ejvhmu/